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Determination of holomorphic modular forms by primitive Fourier coefficients

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Abstract

We prove that Siegel modular forms of degree greater than one, integral weight and level N, with respect to a Dirichlet character \({\chi}\) of conductor \({\mathfrak f_\chi}\) are uniquely determined by their Fourier coefficients indexed by matrices whose contents run over all divisors of \({N/\mathfrak f_\chi}\). The cases of other major types of holomorphic modular forms are included.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyoto University, Kitashirakawa, Kyoto, 606-8502, Japan

    Shunsuke Yamana

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  1. Shunsuke Yamana
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Correspondence to Shunsuke Yamana.

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The author is supported by the Grant-in-Aid for JSPS fellows.

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Yamana, S. Determination of holomorphic modular forms by primitive Fourier coefficients. Math. Ann. 344, 853–862 (2009). https://doi.org/10.1007/s00208-008-0330-4

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  • DOI: https://doi.org/10.1007/s00208-008-0330-4

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